Showers with 3 or 4 stations hit contain sufficient information so their directions can be reconstructed independently of String-21. The rate of such events is 0.002 Hz, approximately 0.3% of the total rate of air-showers in IceTop. Given the angular distribution shown in Fig. 24a, this fraction corresponds to detection of all trajectories that pass within approximately 60 meters of String-21, which is comparable to the size of the muon bundles at a depth of 2000 m. Comparison between the direction assigned to the same events independently by IceTop and by String-21 (zenith angle only) can be used to calibrate the pointing and angular resolution of the deep detector.

To explore this approach, we selected coincident In-Ice and IceTop events with a combined hit multiplicity of at least 8 In-Ice +10 IceTop hits collected during the year 2005. Selected showers were reconstructed with both the IceTop shower reconstruction and the one-string muon track reconstruction discussed in section 4.1. The resulting zenith angle distributions are compared in Fig. 26. Directions obtained with the string reconstruction are systematically closer to the vertical than those obtained with a simple plane fit algorithm to the IceTop showers. Using the shower curvature parameterization of [41], obtained for SPASE (located nearby at the same atmospheric depth and having similar dimensions to the 4-station IceTop array) brings string and IceTop reconstruction results in agreement as shown in Fig. 26 and Fig. 27.